I.(Haran) Arasaratnam, PhD
Finding a solution to nonlinear Bayesian state-estimation problems is intractable and has engaged many researchers
since Kalman’s seminal paper was published in 1960. The selection of suitable sub-optimal approximate solutions to the recursive Bayesian estimation problem represents a trade-off between global optimality on one hand and computational tractability (and robustness) on the other
hand.
I derived a new approximate Bayesian filter for solving discrete-time non-
linear filtering problems efficiently and named the cubature Kalman filter. Here, the term "Cubature" refers to numerical integration in multi-dimensions. Under the assumption that all the conditional densities are Gaussian, the optimal Bayesian filter reduces to the problem
of how to compute multi-dimensional Gaussian-weighted moment integrals present in the time and measurement update steps.
To compute these integrals numerically, a couple of transformations are required: (i) Transform Non-standarad Gaussian weighted integrals to standard Gaussian-weighted integrals using the change of varaiables. (ii) Transform these integrals in the Cartesian coordinate to the spherical-radial coordinate. Subsequently, a a third-degree spherical-radial cubature rule
was prescribed to compute them numerically. The resulting cubature rule entails a set of 2n cubature points, where n is the state-vector dimension. The
cubature Kalman filter is the closest known approximate filter in the sense of preserving second-order information due to the maximum entropy principle. A detailed derivation can be found in IEEE Transactions on Automatic Control published in 2009.
Please see below a complete list of my scholary articles published during the course of my PhD:
PhD Dissertation
- Cubature Kalman Filtering: Theory & Applications, PhD dissertation, ECE Department, McMaster University, April 2009 (PDF)
Patent
- Cognitive tracking Radar, S.Haykin, Z. Amin, I. Arasaratnam & Y.Xue, US Application Serial No 12/588,346, Publication No. 2011/0084871 A1, Canadian Application Serial No 2,682,428, Oct. 2009
Journals
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S. Haykin, A. Zia, Y. Xue, I. Arasaratnam, Control Theoretic Approach to Tracking Radar: First Step Towards Cognition,
Digital Signal Processing, 21(5), pp. 576-585, Sept. 2011 (PDF)
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I. Arasaratnam & S. Haykin, Cubature Kalman Smoothers, Automatica, 47(10), pp. 2245-2250, Oct. 2011 (PDF)
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I. Arasaratnam, S. Haykin & T. Hurd, Cubature Kalman Filtering for Continuous-Discrete Dynamic Systems: Theory & Simulations, IEEE Trans. Signal Processing, 58(10), pp. 1-17, Oct. 2010 (PDF)
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I. Arasaratnam & S. Haykin, Cubature Kalman Filters, IEEE Trans. Automatic Control, 54(6), pp. 1254-1269, June 2009 (PDF)
Book Chapters
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S. Haykin & I. Arasaratnam, Nonlinear Sequential State Estimation for Solving Pattern Classification Problems, Ch. 6,
Adaptive Signal Processing: Next Generation Solutions, T. Adali & S.Haykin, Eds., Wiley-IEEE Press, 2010
(PDF)
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I. Arasaratnam & S. Haykin, Nonlinear Bayesian Filters for Training Recurrent Neural Networks, Advances in Artificial Intelligence, A. Gelbukh & E. Morales, Eds., pp. 12-33, Springer 2008 (PDF)
Conference Papers
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S. Haykin, Z. Amin, I. Arasaratnam, & Y. Xue, Cognitve Tracking Radars, Int'l Radar Conf., Washington DC, USA, May 2010 (Accepted, ID: 9469)
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I. Arasaratnam, & S. Haykin, Cubature Kalman Filtering: A Powerful Tool for Aerospace Applications, Int'l Radar Conf., Bordeaux, France, Oct. 2009
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I. Arasaratnam, S. Haykin, T. Kirubarajan & F. Dilkes, Tracking the Mode of Operations of Multifunction Radars, IEEE Int'l Radar Conf., NY, USA, April 2006
Poster Presentations
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Z. Amin. I. Arasaratnam, & Y. Xue, Cognitive Tracking Radar: A New Generation of Intelligent Radar Systems, McMaster Innovation Showcase, Hamilton, ON, Canada, June 18-19, 2009
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I. Arasaratnam, Cubature Kalman Filtering: A New Practical Tool for Aerospace & Industry, McMaster Innovation Showcase, Hamilton, ON, Canada, June 18-19, 2009
Misc.
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Ph.D. defense slides --> here!
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My PhD Candidacy exam slides --> (UG1,UG2,UG3,UG4,G1,G2,G3)
It includes 4 undergraduate and 3 graduate level questions and answers (Distinction grade awarded)
- Other researchers' commendation letters received after my work appeared on IEEE Journal in 2009 -->
here!